What are the current trends/open questions in logics for knowledge representation?
Some of the work on descriptive logics and modal logics was done within the context of artificial intelligence from a research funding perspective.  Some was part of the normal academic apparatus of mathematics departments.  Furtherance of these fields in the AI context has been hindered by historically low return on investment.

Although first order logic, propositional logic, and fuzzy logic have been investigated conceptually and developed considerably, there are no theorems of note that have been proven without human assistance.  Currently, mathematics is furthered solely by willful acts of humans, although that fact is not immutable.

There have been no proofs offered that artificial machinery cannot ever apply logic to prove theorems, develop disciplines, or assemble new logical systems.  There are also no existing proofs to the contrary.

It is an open question in academia and with governments and corporations investigating the potentials of AI.  To characterize any of the work in progress as a trend would be to exaggerate the effort level along one of many theoretical paths.

A search of academic articles using either descriptive logics and modal logics as search terms, with date constrained to 2008-2018, returns a trend of variety.  Another search of the same decade for articles that reference the twentieth century work in those disciplines produces the same wide distribution.

There is no media hype or academic, corporate, or government claims of any research results that can be translated into useful application.  All of these statistics are research inhibitory.  Investors and educational institutions like paths with clear advantages.

Changes to this condition may come from work being done on the ontological and epistomological side in neural research as it applies to human linguistic networks in the brain.  Although lower animals can appear to draw conclusions, they are largely learning patterns of behavior based on past experience without applying logic.

Dolphins, elephants, dogs, and primates can communicate and exhibit forms of intelligence and personality traits, but existing research indicates that they are unable to learn dialog or develop the ability to form new ideas.

Those investigating semantic approaches in AI seem to exhibit a single orientation, and that may be the one identifiable trend.  They suspect that there is one single causal origin responsible for three things.


The ability to develop complex languages
The ability to construct new schools of thought
The ability to develop a logical argument for or against a proposition or a theory or consider its likelihood logically


There may be something to the idea that natural language rather than formal grammars are the key to higher thinking.